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2000 On the boundedness and decay of moments of solutions to the Navier-Stokes equations
Maria E. Schonbek, Tomas P. Schonbek
Adv. Differential Equations 5(7-9): 861-898 (2000). DOI: 10.57262/ade/1356651290

Abstract

In this paper we consider the existence and decay of moments of the solutions to the Navier-Stokes equations in the whole space ${{\bf R}^n}$; $n \geq 2$ for existence, $2 \leq n \leq 5$ for decay. The decay obtained is algebraic, of order \[ \int_{{{\bf R}^n}} |x|^k |u|^2\,dx \leq C(t+1)^{-2\mu(1-k/n)} \] for $0\leq k\leq n$, for solutions $u$ of appropriate data for which the $L^2$ norm decays at a rate of order $\mu$. That is for solutions that satisfy $||u(t)||_2 \leq C(t+1) ^{-\mu}$. Where $\mu >1/2$. Such solutions are easy to obtain as for example it suffices for $n=3$ that the data $u_0$ is in $L^2 \cap L^1$.

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Maria E. Schonbek. Tomas P. Schonbek. "On the boundedness and decay of moments of solutions to the Navier-Stokes equations." Adv. Differential Equations 5 (7-9) 861 - 898, 2000. https://doi.org/10.57262/ade/1356651290

Information

Published: 2000
First available in Project Euclid: 27 December 2012

zbMATH: 1027.35095
MathSciNet: MR1776344
Digital Object Identifier: 10.57262/ade/1356651290

Subjects:
Primary: 35Q30
Secondary: 35A07 , 35A35 , 35B41 , 76D03 , 76D05

Rights: Copyright © 2000 Khayyam Publishing, Inc.

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Vol.5 • No. 7-9 • 2000
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